Water sorptivity of unsaturated fractured sandstone: Fractal modeling and neutron radiography experiment

The spontaneous imbibition of water into the matrix and gas-filled fractures of unsaturated porous media is an important phenomenon in many geotechnical applications. Previous studies have focused on the imbibition behavior of water in the matrix, but few works have considered spontaneous imbibition along fractures. In this work, a new fractal model, considering the water losses from the fracture to the matrix, was established to predict the sorptivity of rough-walled fracture. A fractal model, considering the fractal dimension of tortuosity, was modified to estimate the sorptivity of the matrix. Both of the models have a time exponent α and can be simplified to the classical Lucas–Washburn (L–W) equation with α = 0.50. To verify the proposed models, quantitative data on the imbibition of water in both the matrix and the fracture of unsaturated sandstone were acquired by neutron radiography. The results show that the motion of the wetting front in both the matrix and the fracture does not obey the L–W equation. Both theory and experimental observations indicate that fracture can significantly increase spontaneous imbibition in unsaturated sandstone by capillary action. Compared with the classical L–W equation, the models proposed in this study offers a better description of the dynamic imbibition behavior of water in unsaturated fractured sandstone and, thus, more reliable predictions of the sorptivity of the matrix and the fracture. Moreover, a new method to estimate the time exponent of rough-walled fracture in sandstone was also provided.